Question

a= 1.2+3.4+.....+99.100

Answer 1

Dặt A =1.2+3.4+.....+99.100

=>3A=1.2.3+2.3.3+3.4.3+....+99.100.3

=>3A=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...99.100(101-98

=>3A=1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 +.....+99.100.101 - 98.99.100

=>3A= 99.100.101

=>A=99.100.101:3

=>A= (99:3).100.101

=>A=33.100.101

=> A=333 300

Answer 2

A=1×2+2×3+3×4+.....+99×100

\(\Leftrightarrow\)3A=1×2×3+2×3×3+3×4×3+....+99×100×3

\(\Leftrightarrow\)3A=1×2×3+2×3×(4-1)+....+99×100×(101-98)

\(\Leftrightarrow\)3A=1×2×3+2×3×4-1×2×3+.....+99×100×101-98×99×100

\(\Leftrightarrow\)3A=99×100×101

\(\Leftrightarrow\)A=\(\frac{99×100×101}{3}\)=33×100×101=333300

Answer 3

a =1.2+3.4+.....+99.100

=>3a=1.2.3+2.3.3+3.4.3+....+99.100.3

=>3a=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...99.100(101-98

=>3a=1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 +.....+99.100.101 - 98.99.100

=>3a= 99.100.101

=>3a:3=99.100.101:3

=>a= (99:3).100.101

=>a=33.100.101

=> a=333 300